Embodiments of the present disclosure relate generally to diagnostic imaging, and more particularly to methods and systems for fast iterative reconstruction using separable system models.
Non-invasive imaging techniques are widely used for diagnostic imaging in applications such as security screening, quality control, and medical imaging systems. Particularly, in medical imaging, a non-invasive imaging technique such as computed tomography (CT) is used for unobtrusive, convenient and fast imaging of underlying tissues and organs. To that end, the CT systems operate by projecting fan or cone shaped X-ray beams through an object. The attenuated beams are then detected by a set of detector elements. Each detector element produces a signal based on the intensity of the attenuated X-ray beams, and these signals are processed to produce projection data, also called sinogram data. Useful images are formed from the projection data with the use of one or more image reconstruction techniques.
In CT, the operation that transforms an N-Dimension image into an M-Dimension set of line integrals is called the forward projection or re-projection, whereas the transpose of this operation is called back-projection. Conventional CT imaging techniques employ direct reconstruction techniques, such as filtered back-projection (FBP) that are generally fast and computationally efficient, as they allow reconstruction of a three-dimensional (3D) image data set in a single reconstruction step. Certain other imaging techniques employ iterative reconstruction algorithms that iteratively update the reconstructed image volume. Use of iterative reconstruction techniques typically provides greater flexibility in selectively enhancing imaging metrics based on specific application requirements.
By way of example, iterative reconstruction techniques provide greater flexibility with respect to acquisition geometry, enforcement of a prior knowledge, and modeling of physical effects, including x-ray source modeling, detector modeling, scatter modeling and/or beam-hardening modeling. Particularly, iterative reconstruction techniques have been employed to improve one or more imaging metrics, such as reducing radiation dose, noise and/or artifacts through iterative processing. By way of example, certain iterative reconstruction techniques perform model-based estimation requiring reconstructions of several images followed by iterative updates of the two or three-dimensional image data set until desired imaging criteria are met.
Iterative reconstruction techniques, however, require enormous amounts of complex computation and may not be efficient in practice unless the volume to be reconstructed is small. In addition, iterative reconstruction techniques are generally much slower than the direct reconstruction techniques. Accordingly, certain techniques have been proposed for reducing the computational cost of iterative reconstruction, such as, ordered subsets, relaxation factors for convergence acceleration, and acceleration of the projector and the back projector.
It is desirable to develop effective methods and systems that enable fast iterative image reconstruction by effectively reducing the required run-time per iteration. Particularly, there is a need for an iterative image reconstruction technique that includes reduced computational requirements and/or improved data access schemes that result in better speed.